Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory

By M. Grossi, Angela Pistoia, Jun-cheng Wei. 2000

102 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/44d22e6b5fdd050b59d6a298f261df5ed64a191b

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005, background): “There exists solutions with an arbitrary large number of peaks (of multibump type) at the boundary and in the interior of ∂Ω, see [8], [12], [15], [16], [18], [22], [37], [39].”
Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity Part I: N=3 (2004, background): “Higher energy solutions exist which blow up at one or several points, located on the boundary [8][13][22][33][19], in the interior of the domain [5][7][11][12][16][21][38][40], or some of them on the boundary and others in the interior [18].”
A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture (2010, background): “Higher energy solutions have also been exhibited, blowing up at one [2], [55], [48], [26] or several separated boundary points [41], [37], [56], Note that by the assumption ( H 2 ), Γ is a circle in the plane y 3 = · · · = y N = 0.”
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005, unknown): “[10], [11], [12], [13], [ 15 ], [17], [24], [26], [28], [29] and references therein.”
Multidimensional boundary layers for a singularly perturbed Neumann problem (2004, background): “Further studies on spike-layer solutions (for the Dirichlet problem as well) can be found in [17], [19], [24], [25], [26], [27], [30], [31], [44], [45].”
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003, background): “[10, 11, 14 , 15, 17, 19, 24 ]a nd references therein.”
Boundary concentration phenomena for a singularly perturbed elliptic problem (2002, background): “This result as well as the uniqueness of Mε was established in [32, 33] and motivated the search of more general solutions of (Pε) concentrating at critical points of H ; see [12, 17, 18, 19, 26, 31, 34, 41].”
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity (2005, background): “This kind of argument has been applied in many other papers (see [12], [36], [19], [22], [24], [41], [42] and references therein).”
The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds (2009, result): “... it has been proved that for any stable critical point of H one can construct single boundary spike layer, while in [10,20,27] the authors construct multiple boundary spike layer solutions at multiple stable critical points of H. Finally, in [12] the authors proved that for any integer k there ex”
Super-critical boundary bubbling in a semilinear Neumann problem (2005, background): “Solutions other than least energy with similar qualita tive behavior around one or several points of the boundary or inside the domain have been found by several authors, see [7,11, 14 ,18,15,19,21,34] and their references.”